A brake system for a motor vehicle may include at least one pressure supply device, formed by a hydraulic piston-cylinder unit driven by an electric motor, for hydraulic adjustment of a brake piston of at least one wheel brake, and at least one electromechanically actuatable wheel brake for electrical adjustment of a brake piston of a wheel brake. An electric motor and a first gearbox, which transmits the driving force of the electric motor to a further gearbox, are provided for electromechanical actuation of the wheel brake. The electromechanically actuatable wheel brake has a hydraulic control device having a piston-cylinder unit, the control piston of which serves for adjusting the brake piston and/or exerting a force on the brake piston. The control piston can be adjusted or a force can be exerted on the control piston.